Abstract
We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times t and low scatterer densities (Boltzmann–Grad limit). The normalization factor is √tlogt, where t is measured in units of the mean collision time. This result holds in any dimension and for a general class of finite-range scattering potentials. We also establish the corresponding invariance principle, i.e., the weak convergence of the particle dynamics to Brownian motion.
Original language | English |
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Pages (from-to) | 933-981 |
Number of pages | 49 |
Journal | Communications in Mathematical Physics |
Volume | 347 |
Issue number | 3 |
Early online date | 18 Feb 2016 |
DOIs | |
Publication status | Published - Nov 2016 |
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Professor Balint A Toth
- School of Mathematics - Chair in Probability
- Probability, Analysis and Dynamics
- Probability
Person: Academic , Member, Group lead